So I have been meditating for a couple of years, generally following tibetan shamata principles.

While I am getting fairly good at dealing with the overall busyness of the mind and, at times, large volume of thoughts, there are some specific thoughts that I don't know how to deal with. That is thoughts about the object of meditation.

For example, if I am following the breath, I might start to think that the breath somehow feels "wrong" or "out of balance". Or if I am simply aware of the contact between my body and the char I am sitting on, I might start to feel that the sensation is, again, "wrong", "off" or out of balance. Like it simply doesn't feel "perfect" as my mind wants it to. And so I start to have a lot of resistance towards my object of meditation. And what do you do then? Simply turning awareness away from the resistance and back to the object of meditation - like I would do with any other thought - doesn't work here, because the object of meditation is what is causing the resistance. So it's a bit of dilemma

I hope you understand what I am trying to explain here.

I was hoping that someone might have some experience with this and/or advice on how to overcome it.

Maybe bring some vipissana/widom aspect to it by investigating where this aversion arises from, where it abides and where it goes? I haven't had this particular experience, so sorry if my suggestion is ridiculous.

Sounds like agitation/tension to me. If you have a tendency to accumulate bodily and mental tension in general, it can be useful to decrease that prior to meditation as I find this can drastically influence how easy it is to rest and feel settled in meditation & life in general.

"And what do you think: when the strings of your vina were neither too taut nor too loose, but tuned[1] to be right on pitch, was your vina in tune & playable?"

"Yes, lord."

"In the same way, Sona, over-aroused persistence leads to restlessness, overly slack persistence leads to laziness. Thus you should determine the right pitch for your persistence, attune[2]the pitch of the [five] faculties [to that], and there pick up your theme."

As an experiment to try with the breath if it feels off balance you can intuitively and gently breathe in such a way that you are addressing the imbalance or discomfort. Rather than it being a problem, see it as your body/mind telling you where you need to loosen or tighten up.

He brings both a very refreshing & scholarly approach to the Dha*ma, and to the fundamental skills of meditation.

One of the things I really enjoy is how he goes "contrarian" on a lot of the current "Buddhist Gestalt" / Consensus Buddhism as some may call it...

Amongst his insightful remarks, is something that goes kind of like this:
"Seeing things as they are" as an mono / one size fits all / "Hammer of an instruction" can make one miss one the crucial insight of the Buddha: Saṅkhāra / "Fabrication" in his lingo !
Things ARE not so much in this or that way... We fabricate / "bake" our experience...
So in your case:
You may want, just for while, to withdraw your attention from the object to look within, and try to see / feel what it it is that you are doing that is making your experience unpleasant, why / where / how you create an experience of aversion... And then release / relax..

Also, another of his interesting difference vis a vis the "consensus":
He strongly advises to play and experiment with the breath (breath energies as he calls them) to gain insight into Saṅkhāra / the fabrication process. (Jhana are, in this perspective, understood as states of less and less fabrication, leading at some point, (as per his lineage of Theravada) to a complete weariness as regards of this endless, never satisfying process of fabrication. In this hiatus one "enters the stream" and experience a glimpse of "the deathless", Nibanna... )

When you are meditating pretty much anything that arises is the same. Meaning whether it's a thought, emotion, or feelings, they are all treated the same way, if you find your mind trying to engage with some phenomena, realize it's no different than how you deal with thoughts, you relax your body, and mind, and let it pass through. You mentioned it's your meditation object it'self.. but is it? Rather it's mental phenomena arising in relation to your meditation object that you are dealing with, realize it's just a trick of the mind.

This is how the mind works -- things arise and your mind latches on to it, and then it goes through a process of clinging or aversion. If your mind enjoys the feeling, it will grasp to it, if it doesn't it will become averse, resulting in more thoughts, and feelings.. the entire process is like a run-away train. Meditation has the end result of stopping this run-away train process. The more you practice, the easier it becomes.

Have you ever had an itch while meditating? These thing's you are describing are EXACTLY like an itch.. you want to scratch it so badly you feel like you can't concentrate anymore. While it takes experience, you can focus on your object, and keep returning to it in a very relaxed way, and the itch eventually fades away.

“Freedom is secured not by the fulfilling of one's desires, but by the removal of desire” – Epictetus

So I have been meditating for a couple of years, generally following tibetan shamata principles.

While I am getting fairly good at dealing with the overall busyness of the mind and, at times, large volume of thoughts, there are some specific thoughts that I don't know how to deal with. That is thoughts about the object of meditation.

For example, if I am following the breath, I might start to think that the breath somehow feels "wrong" or "out of balance". Or if I am simply aware of the contact between my body and the char I am sitting on, I might start to feel that the sensation is, again, "wrong", "off" or out of balance. Like it simply doesn't feel "perfect" as my mind wants it to. And so I start to have a lot of resistance towards my object of meditation. And what do you do then? Simply turning awareness away from the resistance and back to the object of meditation - like I would do with any other thought - doesn't work here, because the object of meditation is what is causing the resistance. So it's a bit of dilemma

I hope you understand what I am trying to explain here.

I was hoping that someone might have some experience with this and/or advice on how to overcome it.

Thanks in advance

Shamata is often practiced in conjunction with vipassana. While shamata helps you concentrate, vipassana leads to insight. Without insight and a certain view of what you are actually doing, meditation can become a struggle. Vipassana is about being aware of whatever it is that is going on. It is not about controlling it or any kind of manipulation. Because of our habit energy, we tend to fixate on things, some more than others, but the process is about being aware of this and not grasping for a change or result to what you 'think' you want or should be. When you engage in this, you begin to have insight into the workings of your mind and begin to let go of many habits. Your object of meditation is not causing any resistance. It is all happening in your mind. The dilemma is your fixation on thought/feeling and your like and dislike. Once you become aware of this through insight, you will more easily move through these moments of fixation. You might even come to the point where there is no problem to fix.

Bussin wrote:
For example, if I am following the breath, I might start to think that the breath somehow feels "wrong" or "out of balance". Or if I am simply aware of the contact between my body and the char I am sitting on, I might start to feel that the sensation is, again, "wrong", "off" or out of balance. Like it simply doesn't feel "perfect" as my mind wants it to. And so I start to have a lot of resistance towards my object of meditation. And what do you do then? Simply turning awareness away from the resistance and back to the object of meditation - like I would do with any other thought - doesn't work here, because the object of meditation is what is causing the resistance. So it's a bit of dilemma

The object of the meditation is not what's causing the resistance! The idea that you have thinking that the sensation needs to be some particular way, is what's causing the resistance, when the sensation does not meet what you think it's supposed to be. Your expectations and judgments of the sensation is what's causing the resistance. You are creating the resistance because you think it's always supposed to be the way you want it to be. Expecting something to always be the way you want it to be...is the perfect recipe for dukkha! So what do you do? Stop judging it and just let it be what it is. Stop demanding that it be "perfect", whatever that means, and just let it be what it is.

One should not kill any living being, nor cause it to be killed, nor should one incite any other to kill. Do never injure any being, whether strong or weak, in this entire universe!